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How to generate the truth table to show that $p \implies (q \vee r)$ is equivalent to $(p \wedge \neg q ) \implies r$ ? Can I use BooleanTable?

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5  
BooleanTable[Implies[p, q || r], {p, q, r}] == BooleanTable[Implies[p && Not[q], r], {p, q, r}] –  belisarius Dec 20 '13 at 0:48
4  
Alternatively, Reduce[Equivalent[Implies[p, q || r], Implies[p && Not[q], r]]] –  Daniel Lichtblau Dec 20 '13 at 0:57

1 Answer 1

(from the comments of belisarius & Daniel Lichtblau)

Equal[
  BooleanTable[Implies[p, q || r], {p, q, r}],
  BooleanTable[Implies[p && Not[q], r], {p, q, r}]
]

(* ==> True *)

Or without truth tables:

Reduce[Equivalent[Implies[p, q || r], Implies[p && Not[q], r]]]

(* ==> True *)
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